Finite Group Databasebeta

← C2×#21455109 #30546442

Subgroups — C2×#21455109 #30546442

Order 15616.

4718 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14519825C211yesmaximal, characteristic
2C22×#14519809C211yesmaximal, characteristic, complemented
3C22×Q16×D61C211yesmaximal, characteristic, complemented
4C2×#16840335C211yesmaximal, characteristic, complemented
5#21455109C2116yesmaximal, direct product factor
6C2×#16839927C211yesmaximal, characteristic, complemented
7C2×#16839926C211yesmaximal, characteristic, complemented
8C2×#16839923C211yesmaximal, characteristic, complemented
9C2×#16839922C211yesmaximal, characteristic, complemented
10C2×#16839919C211yesmaximal, characteristic, complemented
11C2×#16839918C211yesmaximal, characteristic, complemented
12C2×#16839916C211yesmaximal, characteristic, complemented
13C2×#16839769C211yesmaximal, characteristic, complemented
14C2×#16839757C211yesmaximal, characteristic, complemented
15C2×#16839727C211yesmaximal, characteristic, complemented
16C2×C61×#451C211yesmaximal, characteristic, complemented
17C2×#14519825—28no—
18C2×#14519825—24no—
19C2×#14519825—28no—
20C2×#14519825C2218yes—
21C22×#11758226—21no—
22C22×#11758226C2211yescharacteristic
23C22×#11758226C2211yescharacteristic
24C22×#11758222—21no—
25C22×#11758222—21no—
26C22×#11758222C2211yescharacteristic
27C22×#11758222C2211yescharacteristic
28C22×Q8×D61—21no—
29C22×Q8×D61C2211yescharacteristic
30C22×Q8×D61C2211yescharacteristic
31C22×Q8×D61C2211yescharacteristic
32C2×#14519809—28no—
33C2×#14519809C2218yescomplemented
34C22×Dic244C2211yescharacteristic
35C22×#11758202C2211yescharacteristic
36C22×#11758202C2211yescharacteristic
37C22×#11758202C2211yescharacteristic
38C2×Q16×D61—28no—
39C2×Q16×D61C2218yescomplemented
40C22×#11758190C2211yescharacteristic
41C22×#11758201C2211yescharacteristic
42C22×#11758189C2211yescharacteristic
43C22×C8×D61C2211yescharacteristic
44#16840335—24no—
45#16840335C2218yescomplemented
46C2×#14519776—21no—
47C2×#14519763—21no—
48C2×#14519762—21no—
49C2×#14519759—21no—
50C2×#14519757C2211yescharacteristic
51C2×#14519756C2211yescharacteristic
52C2×#14519753C2211yescharacteristic
53C2×#14519735C2211yescharacteristic
54#16839927C2218yescomplemented
55#16839926C2218yescomplemented
56#16839923C2218yescomplemented
57#16839922C2218yescomplemented
58#16839919C2218yescomplemented
59#16839918C2218yescomplemented
60#16839916C2218yescomplemented
61#16839769C2218yescomplemented
62#16839757C2218yescomplemented
63C2×#14519702C2211yescharacteristic
64C2×#14519701C2211yescharacteristic
65C2×#14519701C2211yescharacteristic
66C2×#14519700C2211yescharacteristic
67C2×#14519699C2211yescharacteristic
68C2×#14519697C2211yescharacteristic
69#16839727C2218yescomplemented
70C2×C22⋊#92418C2211yescharacteristic
71C2×#14519689C2211yescharacteristic
72C2×#14519689C2211yescharacteristic
73C23×Q8×C61C2211yescharacteristic
74C22×Q16×C61C2211yescharacteristic
75C22×Q16×C61C2211yescharacteristic
76C2×C22⋊Q8×C61C2211yescharacteristic
77C61×#451C2218yescomplemented
78C2×#103×C61C2211yescharacteristic
79C2×#103×C61C2211yescharacteristic
80C2×C22⋊C8×C61C2211yescharacteristic
81#14519825—264no—
82#14519825—232no—
83#14519825—232no—
84C2×#11758226—216no—
85C2×#11758226—24no—
86C2×#11758226—28no—
87C2×#11758226—24no—
88C2×#11758226—24no—
89C2×#11758226—22no—
90C2×#11758226—22no—
91C2×#11758226D418yes—
92C2×#11758226C2314yes—
93C2×#11758226C2314yes—
94C2×#11758222—216no—
95C2×#11758222—216no—
96C2×#11758222—22no—
97C2×#11758222—28no—
98C2×#11758222—28no—
99C2×#11758222—24no—
100C2×#11758222—24no—
101C2×#11758222—24no—
102C2×#11758222—24no—
103C2×#11758222D414yes—
104C2×#11758222C2314yes—
105C2×#11758222C2314yes—
106C22×Dic122—21no—
107C22×Dic122—21no—
108C22×Dic122—21no—
109C22×Dic122D411yescharacteristic
110C22×Dic122C2311yescharacteristic
111C22×Dic122C2311yescharacteristic
112C2×Q8×D61—216no—
113C2×Q8×D61—24no—
114C2×Q8×D61—24no—
115C2×Q8×D61—22no—
116C2×Q8×D61—22no—
117C2×Q8×D61—22no—
118C2×Q8×D61—28no—
119C2×Q8×D61—24no—
120C2×Q8×D61—24no—
121C2×Q8×D61—24no—
122C2×Q8×D61D418yes—
123C2×Q8×D61C2314yes—
124C2×Q8×D61C2314yes—
125C2×Q8×D61C2314yes—
126C22×D244—21no—
127C22×D244—21no—
128C22×D244D411yescharacteristic
129C22×D244C2311yescharacteristic
130C22×C22⋊D61—21no—
131C22×C22⋊D61D411yescharacteristic
132C22×C22⋊D61D411yescharacteristic
133C22×C4×D61—21no—
134C22×C4×D61—21no—
135C22×C4×D61—21no—
136C22×C4×D61—21no—
137C22×C4×D61—21no—
138C22×C4×D61—21no—
139C22×C4×D61C2311yescharacteristic
140C22×C4×D61C2311yescharacteristic
141#14519809—232no—
142C2×Dic244—24no—
143C2×Dic244C2314yes—
144C2×#11758202—24no—
145C2×#11758202—24no—
146C2×#11758202—24no—
147C2×#11758202C2314yes—
148C2×#11758202C2314yes—
149C2×#11758202C2314yes—
150Q16×D61—232no—
151C2×#11758190—24no—
152C2×#11758190C2314yes—
153C2×#11758201—24no—
154C2×#11758201C2314yes—
155C2×#11758189—24no—
156C2×#11758189C2314yes—
157C22×#92418C2311yescharacteristic
158C22×#92418C2311yescharacteristic
159C2×C8×D61—24no—
160C2×C8×D61C2314yes—
161#14519776—28no—
162#14519763—28no—
163#14519762—28no—
164#14519759—28no—
165#14519757—22no—
166#14519757C2314yes—
167#14519756—22no—
168#14519756C2314yes—
169#14519753—22no—
170#14519753C2314yes—
171#14519735—22no—
172#14519735C2314yes—
173C2×C4⋊Dic61—21no—
174C2×C4⋊Dic61C2311yescharacteristic
175C2×#11758196—21no—
176C2×#11758196—21no—
177C2×C22⋊Dic61—21no—
178C2×#11758198—21no—
179C2×#11758198—21no—
180C2×#11758198—21no—
181C2×C4×Dic61—21no—
182#14519702C2314yes—
183#14519701C2314yes—
184#14519701C2314yes—
185#14519700C2314yes—
186#14519699C2314yes—
187#14519697C2314yes—
188C22⋊#92418C2314yes—
189#14519689C2314yes—
190#14519689C2314yes—
191C22×Q8×C61—24no—
192C22×Q8×C61—24no—
193C22×Q8×C61—21no—
194C22×Q8×C61—22no—
195C22×Q8×C61C2311yescharacteristic
196C22×Q8×C61C2314yes—
197C22×Q8×C61C2311yescharacteristic
198C22×Q8×C61C2311yescharacteristic
199C23×C4×C61—21no—
200C23×C4×C61C2311yescharacteristic
201C2×Q16×C61—24no—
202C2×Q16×C61—24no—
203C2×Q16×C61C2314yes—
204C2×Q16×C61C2314yes—
205C22×C8×C61C2311yescharacteristic
206C22×C8×C61C2311yescharacteristic
207C22⋊Q8×C61—22no—
208C22⋊Q8×C61C2314yes—
209C2×C4⋊C4×C61—21no—
210C2×C4⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61—21no—
212#103×C61C2314yes—
213#103×C61C2314yes—
214C22⋊C8×C61C2314yes—
215C24×C61C2×D411yescharacteristic
216C23×D61—21no—
217C23×D61C2×D411yescharacteristic
218C23×D61C2×D411yescharacteristic
219C2×Q8×C61—28no—
220C2×Q8×C61—216no—
221C2×Q8×C61—28no—
222C2×Q8×C61—28no—
223C2×Q8×C61—22no—
224C2×Q8×C61—22no—
225C2×Q8×C61—24no—
226C2×Q8×C61—21no—
227C2×Q8×C61—21no—
228C2×Q8×C61—21no—
229C2×Q8×C61—22no—
230C2×Q8×C61—22no—
231C2×Q8×C61C2×D414yes—
232C2×Q8×C61C2×D414yes—
233C2×Q8×C61C2412yes—
234C2×Q8×C61C2412yes—
235C2×Q8×C61C2412yes—
236C22×C4×C61—28no—
237C22×C4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—24no—
240C22×C4×C61—22no—
241C22×C4×C61—22no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2412yes—
247C22×C4×C61C2411yescharacteristic
248C2×C22⋊D61—28no—
249C2×C22⋊D61—24no—
250C2×C22⋊D61—24no—
251C2×C22⋊D61—24no—
252C2×C22⋊D61C2×D414yes—
253C2×C22⋊D61C2×D414yes—
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61C2×D411yescharacteristic
258C22×Dic61C2×D411yescharacteristic
259#11758226—264no—
260#11758226—216no—
261#11758226—28no—
262#11758226—28no—
263#11758226—216no—
264#11758226—28no—
265#11758226C2×D4116yes—
266Q8×D61—216no—
267Q8×D61—264no—
268Q8×D61—28no—
269Q8×D61—216no—
270Q8×D61—28no—
271Q8×D61—28no—
272Q8×D61—28no—
273Q8×D61—28no—
274Q8×D61—48no—
275Q8×D61C2×D4116yes—
276#11758222—264no—
277#11758222—216no—
278#11758222—264no—
279#11758222—28no—
280#11758222—216no—
281#11758222—28no—
282#11758222—28no—
283#11758222—28no—
284C2×D244—28no—
285C2×D244—28no—
286C2×D244—24no—
287C2×D244—24no—
288C2×D244—24no—
289C2×D244—21no—
290C2×D244—22no—
291C2×D244C2×D414yes—
292C2×D244C2×D414yes—
293C2×D244C2412yes—
294C2×C4×D61—28no—
295C2×C4×D61—28no—
296C2×C4×D61—28no—
297C2×C4×D61—28no—
298C2×C4×D61—24no—
299C2×C4×D61—24no—
300C2×C4×D61—24no—
301C2×C4×D61—22no—
302C2×C4×D61—22no—
303C2×C4×D61—28no—
304C2×C4×D61—24no—
305C2×C4×D61—24no—
306C2×C4×D61—24no—
307C2×C4×D61—44no—
308C2×C4×D61C2×D412yes—
309C2×C4×D61C2×D412yes—
310C2×C4×D61C2×D414yes—
311C2×C4×D61C2×D414yes—
312C2×C4×D61C2412yes—
313C2×C4×D61C2412yes—
314C2×Dic122—28no—
315C2×Dic122—21no—
316C2×Dic122—22no—
317C2×Dic122—24no—
318C2×Dic122—28no—
319C2×Dic122—24no—
320C2×Dic122—24no—
321C2×Dic122—22no—
322C2×Dic122—22no—
323C2×Dic122—21no—
324C2×Dic122—24no—
325C2×Dic122—44no—
326C2×Dic122C2×D414yes—
327C2×Dic122C2×D414yes—
328C2×Dic122C2412yes—
329C2×Dic122C2412yes—
330Q16×C61—28no—
331Q16×C61—28no—
332C2×C8×C61—22no—
333C2×C8×C61—22no—
334C2×C8×C61C2412yes—
335C2×C8×C61C2412yes—
336C4⋊C4×C61—24no—
337C4⋊C4×C61—21no—
338C4⋊C4×C61C2412yes—
339C22⋊C4×C61—24no—
340C22⋊Dic61—24no—
341#11758202—28no—
342#11758202—28no—
343#11758202—28no—
344#11758201—28no—
345#11758198—24no—
346#11758198—24no—
347#11758198—24no—
348C4⋊Dic61—21no—
349C4⋊Dic61—24no—
350C4⋊Dic61C2412yes—
351#11758196—24no—
352#11758196—24no—
353C4×Dic61—24no—
354C2×#92418—22no—
355C2×#92418—22no—
356C2×#92418C2412yes—
357C2×#92418C2412yes—
358Dic244—28no—
359#11758190—28no—
360#11758189—28no—
361C8×D61—28no—
362C23×C61—22no—
363C23×C61—22no—
364C23×C61—22no—
365C23×C61C22×D412yes—
366C23×C61C22×D411yescharacteristic
367C22×D61—22no—
368C22×D61—22no—
369C22×D61—22no—
370C22×D61—24no—
371C22×D61—22no—
372C22×D61—22no—
373C22×D61—22no—
374C22×D61—42no—
375C22×D61—42no—
376C22×D61#12014yes—
377C22×D61C22×D412yes—
378C22×D61C22×D412yes—
379Q8×C61—216no—
380Q8×C61—24no—
381Q8×C61—24no—
382Q8×C61—22no—
383Q8×C61—22no—
384Q8×C61—22no—
385Q8×C61—22no—
386Q8×C61—42no—
387Q8×C61C22×D414yes—
388Q8×C61C22×D414yes—
389C2×C4×C61—216no—
390C2×C4×C61—24no—
391C2×C4×C61—24no—
392C2×C4×C61—22no—
393C2×C4×C61—22no—
394C2×C4×C61—22no—
395C2×C4×C61—24no—
396C2×C4×C61—22no—
397C2×C4×C61—22no—
398C2×C4×C61—22no—
399C2×C4×C61—22no—
400C2×C4×C61—42no—
401C2×C4×C61—42no—
402C2×C4×C61C22×D412yes—
403C2×C4×C61C22×D411yescharacteristic
404C2×C4×C61C22×D412yes—
405C2×C4×C61C22×D412yes—
406C2×C4×C61C2511yescharacteristic
407C22⋊D61—216no—
408C22⋊D61—28no—
409C22⋊D61—28no—
410C2×Dic61—22no—
411C2×Dic61—24no—
412C2×Dic61—22no—
413C2×Dic61—22no—
414C2×Dic61—22no—
415C2×Dic61—42no—
416C2×Dic61—42no—
417C2×Dic61#12014yes—
418C2×Dic61C22×D412yes—
419C2×Dic61C22×D412yes—
420D244—216no—
421D244—216no—
422D244—28no—
423D244—24no—
424D244—22no—
425D244C22×D414yes—
426C4×D61—216no—
427C4×D61—216no—
428C4×D61—216no—
429C4×D61—216no—
430C4×D61—24no—
431C4×D61—22no—
432C4×D61—22no—
433C4×D61—216no—
434C4×D61—48no—
435C4×D61#12018yes—
436C4×D61C22×D414yes—
437C4×D61C22×D414yes—
438Dic122—216no—
439Dic122—24no—
440Dic122—22no—
441Dic122—216no—
442Dic122—28no—
443Dic122—22no—
444Dic122—22no—
445Dic122—42no—
446Dic122—48no—
447Dic122C22×D414yes—
448C8×C61—22no—
449C8×C61—22no—
450#92418—22no—
451#92418—22no—
452C2×#3011—611nomaximal, Sylow
453C22×C61—22no—
454C22×C61—22no—
455C22×C61—22no—
456C22×C61—44no—
457C22×C61C2×#12012yes—
458C22×C61#57812yes—
459C22×C61#57812yes—
460C22×C61C23×D411yescharacteristic
461C2×D61—28no—
462C2×D61—22no—
463C2×D61—22no—
464C2×D61—22no—
465C2×D61—24no—
466C2×D61—22no—
467C2×D61—22no—
468C2×D61—44no—
469C2×D61—48no—
470C2×D61—42no—
471C2×D61—42no—
472C2×D61C2×#12014yes—
473C4×C61—24no—
474C4×C61—24no—
475C4×C61—22no—
476C4×C61—42no—
477C4×C61—42no—
478C4×C61C2×#12012yes—
479C4×C61C23×D411yescharacteristic
480C4×C61C23×D411yescharacteristic
481Dic61—22no—
482Dic61—24no—
483Dic61—42no—
484Dic61—42no—
485Dic61C2×#12014yes—
486C22×2−1+4—611no—
487C22×#137—611no—
488C23×Q16—611no—
489C2×#536—611no—
490#3011—6116no—
491C2×#452—611no—
492C2×#452—611no—
493C2×#452—611no—
494C2×#452—611no—
495C2×#451—611no—
496C2×#451—611no—
497C2×#451—611no—
498C2×#451D6111yescharacteristic, complemented
499C2×#419—611no—
500C2×#416—611no—
501C2×#408—611no—
502C2×C61—42no—
503C2×C61#301114yescomplemented
504C2×C61C22×#12011yescharacteristic
505C2×C61C2×#57811yescharacteristic
506C2×C61C2×#57811yescharacteristic
507D61—24no—
508D61—42no—
509D61—44no—
510C2×2−1+4—618no—
511C2×2−1+4—1228no—
512C2×2−1+4—1228no—
513C2×2−1+4—1224no—
514C22×#41—611no—
515C22×#41—611no—
516C22×#41—611no—
517C22×#41—611no—
518C22×#41—1221no—
519C22×#41—1221no—
520C22×#41—1221no—
521C23×Q8—611no—
522C23×Q8—611no—
523C23×Q8—611no—
524C23×Q8—1221no—
525C23×Q8C2×D6111yescharacteristic
526C2×#137—618no—
527C2×#137—1228no—
528C22×Q16—611no—
529C22×Q16—611no—
530C22×Q16—611no—
531C22×Q16—618no—
532C22×Q16—611no—
533C22×Q16—1228no—
534C22×Q16C2×D6111yescharacteristic
535C22×Q16C2×D6111yescharacteristic
536C22×SD16—611no—
537C22×SD16—611no—
538C22×M16—611no—
539C23×C8—611no—
540#536—618no—
541#536—1224no—
542C2×C4⋊Q8—1221no—
543C2×#124—1221no—
544C2×#123—1221no—
545C2×#123—1221no—
546C2×C22⋊Q8—611no—
547C2×C22⋊Q8—611no—
548C2×C22⋊Q8—611no—
549C2×C22⋊Q8C2×D6111yescharacteristic
550C2×#117—611no—
551#452—618no—
552#452—618no—
553#452—618no—
554#452—618no—
555#451—618no—
556#451—618no—
557#451—618no—
558#451C2×D6118yescomplemented
559#419—618no—
560#416—618no—
561C2×#103—611no—
562C2×#103—611no—
563C2×#103—611no—
564C2×#103—611no—
565C2×#103C2×D6111yescharacteristic
566C2×#103C2×D6111yescharacteristic
567C2×#102—611no—
568C2×#102—611no—
569#408—618no—
570C2×C22⋊C8—611no—
571C2×C22⋊C8—611no—
572C2×C22⋊C8—611no—
573C2×C22⋊C8C2×D6111yescharacteristic
574C61C2×#301111yescharacteristic, complemented, Sylow
5752−1+4—12232no—
5762−1+4—12232no—
5772−1+4—12264no—
578C2×#41—614no—
579C2×#41—614no—
580C2×#41—618no—
581C2×#41—614no—
582C2×#41—614no—
583C2×#41—614no—
584C2×#41—1224no—
585C2×#41—1224no—
586C2×#41—1224no—
587C2×#41—1228no—
588C2×#41—1228no—
589C2×#41—1224no—
590C2×#41—12216no—
591C2×#41—12216no—
592C2×#41—1222no—
593C2×#41—1224no—
594C2×#41—1222no—
595C2×#41—1224no—
596C2×#41—1228no—
597C2×#41—12216no—
598C2×#41—1224no—
599C2×#41—1222no—
600C22×Q8—24no—
601C22×Q8—24no—
602C22×Q8—21no—
603C22×Q8—22no—
604C22×Q8—611no—
605C22×Q8—618no—
606C22×Q8—614no—
607C22×Q8—614no—
608C22×Q8—614no—
609C22×Q8—611no—
610C22×Q8—611no—
611C22×Q8—1221no—
612C22×Q8—1221no—
613C22×Q8—1221no—
614C22×Q8—1222no—
615C22×Q8—1224no—
616C22×Q8—1222no—
617C22×Q8—1222no—
618C22×Q8—1224no—
619C22×Q8—1224no—
620C22×Q8—1224no—
621C22×Q8—1228no—
622C22×Q8—12216no—
623C22×Q8—1224no—
624C22×Q8C22×D6111yescharacteristic
625C22×Q8C22×D6114yes—
626C22×Q8C22×D6111yescharacteristic
627C22×Q8C22×D6111yescharacteristic
628C22×D4—611no—
629C22×D4—611no—
630C22×D4—611no—
631C22×D4—611no—
632C22×D4—1221no—
633C22×D4—1221no—
634C22×D4—1221no—
635C23×C4—21no—
636C23×C4—611no—
637C23×C4—611no—
638C23×C4—1221no—
639C23×C4—1221no—
640C23×C4—1221no—
641C23×C4—1221no—
642C23×C4—1221no—
643C23×C4—1221no—
644C23×C4C22×D6111yescharacteristic
645#137—12232no—
646C2×Q16—24no—
647C2×Q16—24no—
648C2×Q16—614no—
649C2×Q16—614no—
650C2×Q16—614no—
651C2×Q16—614no—
652C2×Q16—1224no—
653C2×Q16—12232no—
654C2×Q16—1224no—
655C2×Q16—1224no—
656C2×Q16—1224no—
657C2×Q16C22×D6114yes—
658C2×Q16C22×D6114yes—
659C2×SD16—614no—
660C2×SD16—614no—
661C2×SD16—1224no—
662C2×SD16—1224no—
663C2×M16—614no—
664C2×M16—1224no—
665C22×C8—611no—
666C22×C8—611no—
667C22×C8—614no—
668C22×C8—1224no—
669C22×C8C22×D6111yescharacteristic
670C22×C8C22×D6111yescharacteristic
671C4⋊Q8—1228no—
672#124—1228no—
673#123—1228no—
674#123—1228no—
675C22⋊Q8—22no—
676C22⋊Q8—614no—
677C22⋊Q8—614no—
678C22⋊Q8—614no—
679C22⋊Q8—1222no—
680C22⋊Q8—1222no—
681C22⋊Q8—1222no—
682C22⋊Q8C22×D6114yes—
683#117—614no—
684#117—1222no—
685C2×C4⋊C4—21no—
686C2×C4⋊C4—611no—
687C2×C4⋊C4—1221no—
688C2×C4⋊C4—1221no—
689C2×C4⋊C4—1221no—
690C2×C4⋊C4C22×D6111yescharacteristic
691C2×C22⋊C4—21no—
692C2×C22⋊C4—1221no—
693C2×C22⋊C4—1221no—
694C2×C22⋊C4—1221no—
695C2×C22⋊C4—1221no—
696C2×C42—1221no—
697#103—614no—
698#103—614no—
699#103—614no—
700#103—614no—
701#103C22×D6114yes—
702#103C22×D6114yes—
703#102—614no—
704#102—614no—
705C22⋊C8—614no—
706C22⋊C8—614no—
707C22⋊C8—614no—
708C22⋊C8C22×D6114yes—
709C24—611no—
710C24—611no—
711C24—1221no—
712C24D4×D6111yescharacteristic
713#41—6116no—
714#41—12216no—
715#41—1228no—
716#41—1228no—
717#41—1228no—
718#41—1228no—
719#41—12264no—
720#41—12264no—
721#41—12216no—
722#41—12216no—
723#41—1228no—
724#41—1228no—
725#41—12264no—
726#41—12216no—
727#41—1228no—
728C2×Q8—28no—
729C2×Q8—216no—
730C2×Q8—28no—
731C2×Q8—28no—
732C2×Q8—22no—
733C2×Q8—22no—
734C2×Q8—24no—
735C2×Q8—21no—
736C2×Q8—21no—
737C2×Q8—21no—
738C2×Q8—22no—
739C2×Q8—22no—
740C2×Q8—614no—
741C2×Q8—6116no—
742C2×Q8—614no—
743C2×Q8—612no—
744C2×Q8—612no—
745C2×Q8—1228no—
746C2×Q8—1224no—
747C2×Q8—1224no—
748C2×Q8—1224no—
749C2×Q8—1224no—
750C2×Q8—1228no—
751C2×Q8—12216no—
752C2×Q8—1228no—
753C2×Q8—1228no—
754C2×Q8—1228no—
755C2×Q8—1228no—
756C2×Q8—12264no—
757C2×Q8—12216no—
758C2×Q8—1228no—
759C2×Q8—1222no—
760C2×Q8—1221no—
761C2×Q8—1221no—
762C2×Q8—1222no—
763C2×Q8—1222no—
764C2×Q8—2444no—
765C2×Q8—2448no—
766C2×Q8D4×D6114yes—
767C2×Q8D4×D6114yes—
768C2×Q8C23×D6112yes—
769C2×Q8C23×D6112yes—
770C2×Q8C23×D6112yes—
771C2×D4—614no—
772C2×D4—614no—
773C2×D4—614no—
774C2×D4—614no—
775C2×D4—612no—
776C2×D4—1224no—
777C2×D4—1228no—
778C2×D4—1224no—
779C2×D4—1224no—
780C2×D4—1228no—
781C2×D4—1224no—
782C2×D4—1224no—
783C2×D4—1228no—
784C2×D4—1224no—
785C2×D4—1221no—
786C2×D4—1222no—
787C22×C4—28no—
788C22×C4—24no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—22no—
792C22×C4—22no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—611no—
796C22×C4—612no—
797C22×C4—614no—
798C22×C4—614no—
799C22×C4—612no—
800C22×C4—611no—
801C22×C4—612no—
802C22×C4—612no—
803C22×C4—1228no—
804C22×C4—1224no—
805C22×C4—1224no—
806C22×C4—1228no—
807C22×C4—1224no—
808C22×C4—1224no—
809C22×C4—1228no—
810C22×C4—1228no—
811C22×C4—1228no—
812C22×C4—1224no—
813C22×C4—1221no—
814C22×C4—1222no—
815C22×C4—1222no—
816C22×C4—1224no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—2444no—
820C22×C4D4×D6112yes—
821C22×C4D4×D6111yescharacteristic
822C22×C4C23×D6112yes—
823C22×C4C23×D6111yescharacteristic
824Q16—28no—
825Q16—28no—
826Q16—1228no—
827Q16—1228no—
828Q16—1228no—
829Q16—1228no—
830SD16—1228no—
831SD16—1228no—
832M16—1228no—
833C2×C8—22no—
834C2×C8—22no—
835C2×C8—612no—
836C2×C8—612no—
837C2×C8—1228no—
838C2×C8—1222no—
839C2×C8—1222no—
840C2×C8C23×D6112yes—
841C2×C8C23×D6112yes—
842C4⋊C4—24no—
843C4⋊C4—21no—
844C4⋊C4—612no—
845C4⋊C4—1224no—
846C4⋊C4—1224no—
847C4⋊C4—1221no—
848C4⋊C4—1224no—
849C4⋊C4C23×D6112yes—
850C22⋊C4—24no—
851C22⋊C4—1224no—
852C22⋊C4—1224no—
853C22⋊C4—1224no—
854C22⋊C4—1224no—
855C42—1224no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—614no—
860C23—612no—
861C23—612no—
862C23—1222no—
863C23—1222no—
864C23—1224no—
865C23—1222no—
866C23—1222no—
867C23—1222no—
868C23—1222no—
869C23—2442no—
870C23—2442no—
871C23C2×D4×D6112yes—
872C23C2×D4×D6111yescharacteristic
873Q8—216no—
874Q8—24no—
875Q8—24no—
876Q8—22no—
877Q8—22no—
878Q8—22no—
879Q8—22no—
880Q8—42no—
881Q8—614no—
882Q8—12216no—
883Q8—1228no—
884Q8—12216no—
885Q8—1224no—
886Q8—1222no—
887Q8—1222no—
888Q8—1222no—
889Q8—2448no—
890Q8—2442no—
891Q8C2×D4×D6114yes—
892Q8C2×D4×D6114yes—
893D4—614no—
894D4—1228no—
895D4—12216no—
896D4—12216no—
897D4—1228no—
898D4—1228no—
899D4—12216no—
900D4—1224no—
901D4—1222no—
902C2×C4—216no—
903C2×C4—24no—
904C2×C4—24no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—24no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—614no—
916C2×C4—612no—
917C2×C4—618no—
918C2×C4—614no—
919C2×C4—614no—
920C2×C4—612no—
921C2×C4—12216no—
922C2×C4—12216no—
923C2×C4—12216no—
924C2×C4—12216no—
925C2×C4—12216no—
926C2×C4—1222no—
927C2×C4—1224no—
928C2×C4—1222no—
929C2×C4—1224no—
930C2×C4—1222no—
931C2×C4—1222no—
932C2×C4—1222no—
933C2×C4—1222no—
934C2×C4—2448no—
935C2×C4—2442no—
936C2×C4—2442no—
937C2×C4C2×D4×D6112yes—
938C2×C4C2×D4×D6111yescharacteristic
939C2×C4C2×D4×D6112yes—
940C2×C4C2×D4×D6112yes—
941C2×C4C24×D6111yescharacteristic
942C8—22no—
943C8—22no—
944C8—1222no—
945C8—1222no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—44no—
950C22—614no—
951C22—1228no—
952C22—1222no—
953C22—1222no—
954C22—1224no—
955C22—1222no—
956C22—1222no—
957C22—1222no—
958C22—2444no—
959C22—2448no—
960C22—2442no—
961C22—2442no—
962C22#120×D6112yes—
963C22#1684057512yes—
964C22#1684057812yes—
965C22C22×D4×D6111yescharacteristic
966C4—24no—
967C4—24no—
968C4—22no—
969C4—42no—
970C4—42no—
971C4—614no—
972C4—1222no—
973C4—1224no—
974C4—2442no—
975C4—2442no—
976C4#120×D6112yes—
977C4C22×D4×D6111yescharacteristic
978C4C22×D4×D6111yescharacteristic
979C2—42no—
980C2—1224no—
981C2—2442no—
982C2—2444no—
983C2#2145510914yesdirect product factor
984C2C2×#120×D6111yescharacteristic
985C2C2×#1684057511yescharacteristic
986C2C2×#1684057811yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#451C2
socleC23×C61C22×D4
prime radicalC22×#14519825C2
hypercenterC2×#451D61
hypocenterC61C2×#3011
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C22×#14519809C2semidirect
3. C22×Q16×D61C2semidirect
4. C2×#16840335C2semidirect
5. #21455109C2direct (N × H)
6. C2×#16839927C2semidirect
7. C2×#16839926C2semidirect
8. C2×#16839923C2semidirect
9. C2×#16839922C2semidirect
10. C2×#16839919C2semidirect
11. C2×#16839918C2semidirect
12. C2×#16839916C2semidirect
13. C2×#16839769C2semidirect
14. C2×#16839757C2semidirect
15. C2×#16839727C2semidirect
16. C2×C61×#451C2semidirect
33. C2×#14519809C22semidirect
39. C2×Q16×D61C22semidirect
45. #16840335C22semidirect
54. #16839927C22semidirect
55. #16839926C22semidirect
56. #16839923C22semidirect
57. #16839922C22semidirect
58. #16839919C22semidirect
59. #16839918C22semidirect
60. #16839916C22semidirect
61. #16839769C22semidirect
62. #16839757C22semidirect
69. #16839727C22semidirect
77. C61×#451C22semidirect
498. C2×#451D61semidirect
503. C2×C61#3011semidirect
558. #451C2×D61semidirect
574. C61C2×#3011semidirect
983. C2#21455109direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145198252
C22×#145198092
C22×Q16×D612
C2×#168403352
#214551092
C2×#168399272
C2×#168399262
C2×#168399232
C2×#168399222
C2×#168399192
C2×#168399182
C2×#168399162
C2×#168397692
C2×#168397572
C2×#168397272
C2×C61×#4512
C2×#301161